3.3 - Work, Energy And Power

Question 1

What is work done?

Answer 1

• energy transferred
• force x distance moved in the direction of the force
• measured in Nm or joules

Question 2

What is a joule?

Answer 2

• the work done when a force of 1N moves its point of application 1m in the direction of that force

Question 3

What are the equations for work done by a force?

Answer 3

W = Fx

W = Fxcosθ

W = work done 
F = force
x = distance moved

Question 4

What is energy?

Answer 4

• the capacity for doing work
• scalar quantity
• SI unit = the joule

Question 5

What is the principle of conservation of energy?

Answer 5

The total energy of a closed system remains constant; energy can never be created or destroyed, but in van be transferred from one form to another

Question 6

What is kinetic energy?

Answer 6

• energy due to the motion of an object with mass

- eg moving car, moving atoms

Question 7

What is gravitational potential energy?

Answer 7

• energy of an object due to its position in a gravitational field
• eg child at top of slide, water in clouds

Question 8

What is elastic potential energy?

Answer 8

• energy stirred in an object as a result of reversible change in its shape
• eg a stretched guitar string, a squashes spring

Question 9

What is electrical potential energy

Answer 9

• energy of electrical charged due to their position in an electrical field
• eg electrical charges on a thundercloud, static charge on a charged balloon

Question 10

What is nuclear energy?

Answer 10

• energy within the nuclei of atoms
• it can be released when particles within the nucleus are rearranged
• eg energy from nuclear fission stations, nuclear fusion processes in the sun

Question 11

What is radiant energy?

Answer 11

• aka electromagnetic energy, radiation
• energy associated with all EM waves, stored within oscillating electric and magnetic fields
• eg energy from the sun, energy from an LED

Question 12

What is sound energy?

Answer 12

• energy of mechanical longitudinal waves due to the movement of atoms
• eg energy from loudspeaker, clapping your hands

Question 13

What is thermal energy?

Answer 13

• the sum of random potential and kinetic energies of atoms in a system
• eg a hot cup of tea has more energy than a cold one

Question 14

What is the equation for kinetic energy?

Answer 14

Ek = 1/2mv^2

Ek = kinetic energy (work done), joules
m = mass, kg
v = speed, ms^-1

Note: for objects travelling at the same speed, Ek is directly proportional to mass. For objects of the same mass, Ek is directly proportional to speed squared.

Question 15

What happens when a force is applied to an object at rest?

Answer 15

• the force causes it to accelerate.

- the work done by this force is equal to the kinetic energy transferred to the object.

Question 17

What is the equation for gravitational potential energy in a uniform gravitational field?

Answer 17

Ep = mg Δh

Ep = GPE (gravitational potential energy), joules
m = mass, kg
g = gravitational field strength (acceleration of free fall), m/s² 
Δh = change in height, metres

Note: GPE is gained when an object gets higher and lost when an object gets lower

Question 18

How is the equation for GPE derived?

Answer 18

1) W=Fd

2) force of an object = weight = mg
Sub in: W = mgd

3) distance travelled = change in height

W=mgΔh
Ep = mgΔh

Question 19

State and explain the equation derived from the exchange between GPE and KE

Answer 19

v = √2gΔh
Where v = the final speed of the object

This is because if all GPE is transferred to KE:
1/2mv² = mgΔh

M cancels out:
1/2v² = gΔh

Rearrange:
v² = 2gΔh
v = √2gh

Question 20

Define power generated by a force

Answer 20

Power generated by a force is the rate of work done

Question 21

What are the equations for mechanical power?

Answer 21

P=W/t

P= power, watts/Joules per second
W= work done, joules
t=time, seconds

P=fv

P= power
f = force
v = velocity

Question 22

Define the watt

Answer 22

The power generated when one joule of energy is transferred each second.

Question 23

How is the equation P=vt derived?

Answer 23

1) P = W/t
W = Fd
P = Fd/t

2) d/t = v
P = Fv

This equation can be used whenever a force is required to keep an object at a constant velocity eg a car, swimmer in water, skydiver falling through air at terminal velocity

Question 24

What is efficiency?

Answer 24

The percentage of energy/power that is converted into a useful output (while energy is conserved, not all energy is transferred to useful forms)

Question 25

What is the equation for efficiency?

Answer 25

Efficiency = (useful output energy/total input energy) x 100

Or

Efficiency = (useful output power/total input power) x 100

Question 26

How is the equation for kinetic energy derived?

Answer 26

1) Rearrange v² =u² + 2as to make s subject (u = 0) to get s = v²/2a
2) sub s into W=Fd to get W = F v²/2a
3) sub in F = ma to get W=(mav²)/2a
4) acceleration cancels, W=(mv²)/2 = 1/2mv²